1. Field of the invention
The arterial system consists largely of curved and branching vessels. Arterial flow is generally laminar but is strongly influenced by inertial forces (Reynolds numbers&gt;&gt;1). Almost all studies of arterial fluid dynamics consider the curvature and branching to be planar. The mechanics of steady flow (Reynolds number&gt;&gt;1) in planar bends and branches are reasonably well understood and involve:
secondary motion in the plane of the bend or bifurcation; low wall shear at the inner wall of the bend (where flow separation may occur) and high wall shear at the outer wall; and low wall shear at the outer wall of a branch (where flow separation may occur) together with high wall shear at the inner wall (flow divider).
2. Description of the Related Art
Several findings indicate that the local blood velocity field influences: (a) the dimensions and mechanical properties of vessels and the morphology, mechanics and metabolism of the endothelium (Yoshida et al, 1988), and (b) the development of vascular disease, in particular atherosclerosis (which causes heart attack and stroke) which develops preferentially in low shear regions in arteries (Yoshida et al, 1988); intimal hyperplasia (which causes the occulusion of vascular grafts) and which develops preferentially in low shear regions in side-to-side veno-arterial bypass grafts (Dobrin et al, 1988; Rittgers and Bhambhani, 1993), and thrombosis which occurs preferentially in low shear regions.
There has been limited consideration in the physiological literature of the mechanics of flow in non-planar bends and branches.
The aortic arch is recognised to curve three-dimensionally and rotational flow has been detected in the aortic arch and descending thoracic aorta (Caro et al, 1971; Frazin et al, 1990).
The branching of the left common coronary artery is recognised to be non-planar and studies in a curved bifurcation model show skewing of the velocity profile away from the `plane` of bifurcation, both upstream of the bifurcation and in a daughter tube (Batten and Nerem, 1982).
Studies of the velocity field in a realistic model of the abdominal aorta and aortic bifurcation show centrifugal effects caused by the curvature of the abdominal aorta and aortic bifurcation inducing helical flow structures and influencing the localisation of separation zones (Pedersen et al, 1992).
There has been study of the exact anatomical locations of atherosclerotic lesions and of the detailed flow patterns at these locations in transparent isolated human arteries (Asakura and Karino, 1990).